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Using an identity, what is the value of \( 96\times104 \)?
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Answer and explanation
Correct answer: 9984
Here, \(96=100-4\) and \(104=100+4\). Therefore, \((100-4)(100+4)=100^2-4^2=10000-16=9984\). The option \(10016\) results from adding \(4^2\) instead of subtracting it. Exam tip: when two numbers are equally spaced around a middle number, use \((a-b)(a+b)=a^2-b^2\).
Frequently asked questions
What is the correct answer to this question?
9984
Why is this the correct answer?
Here, \(96=100-4\) and \(104=100+4\). Therefore, \((100-4)(100+4)=100^2-4^2=10000-16=9984\). The option \(10016\) results from adding \(4^2\) instead of subtracting it. Exam tip: when two numbers are equally spaced around a middle number, use \((a-b)(a+b)=a^2-b^2\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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